Question

The temperatures of two bodies measured by a thermometer are $t_{1}=20\,{}^{\circ}C \pm0.5\,{}^{\circ}C$ and $t_{2}=50\,{}^{\circ}C \pm0.5\,{}^{\circ}C$. The temperature difference and the error there in is

• A. $30\,{}^{\circ}C \pm1\,{}^{\circ}C $
• B. $70\,{}^{\circ}C \pm 0.5\,{}^{\circ}C $
• C. $30\,{}^{\circ}C \pm 0.5\,{}^{\circ}C $
• D. $70\,{}^{\circ}C \pm 1\,{}^{\circ}C $

Answer 1

Answer: (A)

Here, $t_{1}=20\,{}^{\circ}C \pm0.5\,{}^{\circ}C$ ;
$t_{2}=50\,{}^{\circ}C \pm0.5\,{}^{\circ}C$
The temperature difference of two bodies is
$t=t_{2}-t_{1}=50\,{}^{\circ}C -20\,{}^{\circ}C =30\,{}^{\circ}C $
The error in temperature difference is given by
$\Delta t=\left(\Delta t_{1}+\Delta t_{2}\right)=\left(0.5\,{}^{\circ}C+0.5\,{}^{\circ}C\right)=1\,{}^{\circ}C$
$\therefore $ The temperature difference is $30\,{}^{\circ}C \pm1\,{}^{\circ}C$.